Simulating electrostrictive deformable mirrors: II. Nonlinear dynamic analysis

Abstract

In this study, we developed a simple electromechanical, lumped parameter model to simulate the dynamic performance of a deformable mirror driven by electrostrictive actuators in an adaptive optics system. Positioned behind the mirror, the multilayered actuator array dynamically controls the mirror's surface shape for optical phase compensation. Our analysis approach combined the linear mechanical impedance of the mirror with a nonlinear representation of an actuator in the array. We used a nonlinear constitutive law for the electrostrictive material to accurately characterize prestress and bias voltage effects on the actuator's induced strain behavior. The model examines the effect of the mirror's impedance on the actuator's resonance characteristics, and predicts the dynamic range limitation imposed by the mechanical structure of the device. The nonlinear behavior of the actuator material created super-harmonics that limited the operational bandwidth of the deformable mirror. However, the analysis showed that tuning the actuator's bias voltage significantly reduced or eliminated these super-harmonics. The model also clearly demonstrated that this tuning does not adversely affect the device's displacement output, power consumption or efficiency.